AI in Mathematics: Analysis of the 2026 IMO Results and the Rise of Autonomous Agents
The recent conclusion of the 67th International Mathematical Olympiad (IMO) marked a historic milestone for both human competitors and artificial intelligence. While the Chinese team secured first place with a total score of 232 points—including three individual perfect scores—a parallel development on GitHub revealed that autonomous AI systems have now surpassed even this elite human performance.
Former Google engineer Deedy Das conducted an independent benchmark of seven state-of-the-art Large Language Models (LLMs) on the IMO 2026 exam. The results were staggering: multiple frontier models, including Claude Fable 5, GPT-5.6 Sol, Kimi K3, and AxiomProver, achieved perfect scores (42/42) on all six problems autonomously.
The Metrics of Intelligence: Efficiency vs. Capability
The benchmark highlights distinct trade-offs between computational efficiency, speed, and resource consumption among the top-performing models. These metrics offer a fascinating look into how different architectures approach complex problem-solving.
Top Performers
- Claude Fable 5: This model demonstrated a strong balance of speed and capability. It achieved a perfect score in just 2.5 hours, consuming approximately $51 USD. Utilizing 9 conversation turns and generating roughly 700,000 tokens, its most challenging task was Problem 3, which required a single inference of 73 minutes.
- GPT-5.6 Sol (xhigh version): Also securing a perfect 42/42, GPT-5.6 Sol emerged as the most resource-efficient model regarding token generation. It produced only 230,000 tokens—less than one-third of what Claude used—across 3.8 hours for a cost of just $20 USD. However, efficiency came with stability challenges; the model experienced network interruptions and spent 106 minutes on Problem 2.
- Kimi K3: As a massive Mixture of Experts (MoE) model with 2.8 trillion parameters, Kimi K3 proved it has the raw power to solve the hardest math problems. However, it required significantly more resources: 17.4 hours, $31 USD, and 1.54 million tokens (6.5 times more than GPT-5.6 Sol). For a single problem (Problem 3), it needed 6 attempts spanning over 8 hours.
- AxiomProver: Independently submitted by the benchmark organizers, this model also reached the maximum score, validating the robustness of the results.
The Bottleneck: Grok 4.5
In stark contrast, Grok 4.5 struggled significantly, particularly with Problem 6—the final number theory problem from Day 2. During the actual 2025 competition, only 6 human participants managed to solve this specific problem.
While Grok 4.5 is a powerful model, it produced only 7,053 tokens for this section and failed to provide a complete proof. It recorded a minimal cost of $0.18 but ultimately submitted an incomplete result, noting, "Full proof: (Not yet complete.)"
Technical Deep Dive: How AI Thinks About Math
The benchmark reveals divergent algorithmic strategies employed by the models to solve identical problems. By analyzing their approaches, we can see how different logical frameworks converge on the same truths.
Case Study: Problem 1 (Divisibility and Termination)
This problem involved an operation on integers using Greatest Common Divisor (gcd) and Least Common Multiple (lcm). The challenge required proving that the process terminates and identifying the invariant value.
- Claude Fable 5 Strategy: Claude utilized a constructed counter function, $\Phi = T + N$, where $T$ represents the sum of prime factors and $N$ is the count of integers greater than 1. It successfully proved that $\Phi$ decreases by at least 1 per step, ensuring finite termination.
- GPT-5.6 Sol Strategy: GPT employed a lexicographical ordering approach using two variables: Product ($P$) and Count ($K$). It demonstrated that the pair $(P, K)$ strictly decreases lexicographically because either the product decreases or the count of numbers greater than 1 decreases.
Despite these different mathematical paths, both models converged on the exact same invariant for the final value $M$: the product of primes raised to the power of the gcd of their exponents across all numbers on the board.
Case Study: Problem 6 (Number Theory Periodicity)
This problem served as the major differentiator between the models.
* Claude Fable 5 solved it in 26 minutes over two turns.
* GPT-5.6 Sol completed it in 60 minutes over two turns.
* Kimi K3 required 381 minutes over four turns.
* Grok 4.5 failed to generate a valid proof entirely.
Agent Capability vs. Model Intelligence
A critical finding from this test is the distinction between raw mathematical capability and Agent capability—specifically, the ability to use tools effectively.
Grok 4.5's failure was attributed not to a lack of mathematical logic, but to a breakdown in tool-use execution. The model claimed to have written the proof to a file but failed to actually invoke the file-writing tool. This highlights a persistent and significant challenge in autonomous AI systems: bridging the gap between internal reasoning and external action execution. An AI can know the answer, but if it cannot reliably execute the tools to deliver that answer, the intelligence remains trapped.
Historical Context and Industry Implications
The progression of AI in mathematics over the last three years has been nothing short of exponential:
- 2024: DeepMind's AlphaProof reached the silver medal level, showing AI could compete with top humans.
- 2025: OpenAI and DeepMind released models capable of solving 5 out of 6 problems, reaching Gold Medal tier.
- 2026: General-purpose LLMs without specialized mathematical training have now achieved perfect scores.
The Infrastructure of Automation
This feat was facilitated by Axiom Math, a company founded by 25-year-old Hong Letong, a Morgan Prize winner and MIT graduate. Axiom Math translated the IMO 2026 questions into machine-readable Lean 4 formalizations. This allowed for automated compilation and grading, removing human subjectivity from the evaluation process.
The financial markets have taken notice. Axiom Math recently closed a $200 million Series A round, valuing the company at $1.6 billion. This valuation underscores the immense commercial interest in automating high-level verification tasks.
Broader Applications: Beyond Math Competitions
The ability of these models to execute long-chain logical deduction without errors translates directly to complex professional workflows. The implications extend far beyond mathematics competitions. Tasks previously requiring human experts for high-stakes verification are now within the reach of consumer-grade AI products.
Specifically, industries relying on rigorous compliance and logic—such as contract auditing, insurance claim verification, and tax regulation checks—are poised for disruption. If an LLM can solve the hardest problems in the IMO, it can certainly navigate the complexities of corporate compliance, doing so faster, cheaper, and with fewer errors than human auditors.
As we move further into 2026, the line between human expert capability and AI autonomy continues to blur. The question is no longer if AI can solve these problems, but how quickly we can integrate these capabilities into the infrastructure of our economy.